Vital Spreaders Identification in Complex Networks with Multi-Local Dimension

The important nodes identification has been an interesting problem in this issue. Several centrality measures have been proposed to solve this problem, but most of previous methods have their own limitations. To address this problem more effectively, multi-local dimension (MLD) which is based on the fractal property is proposed to identify the vital spreaders in this paper. This proposed method considers the information contained in the box and $q$ plays a weighting coefficient for this partition information. MLD would have different expressions with different value of $q$, and it would degenerate to local information dimension and variant of local dimension when $q = 1$ when $q = 0$ respectively, both of which have been effective identification method for influential nodes. Thus, MLD would be a more general method which can degenerate to some exiting centrality measures. In addition, different with classical methods, the node with low MLD would be more important in the network. Some comparison methods and real-world complex networks are applied in this paper to show the effectiveness and reasonableness of this proposed method. The experiment results show the superiority of this proposed method.